Data stored in magnetic or optical disks are usually protected by so-called Reed-Solomon (RS) codes. Whenever the redundancy of a RS code is 2t bytes, the code can correct up to s bytes in error and e erased bytes, where 2s+e.ltoreq.2t. It will be assumed that a byte consists of 8 bits; hence RS codes over GF(256) will be considered.
Normally, the user data are divided into sectors, each consisting of 512 user bytes. Since noise in the channel affects recovery of these user bytes, redundancy is added to them using a RS code. A common strategy is to divide a sector into eight strings of information bytes, each string having 64 bytes, and to encode each string; then the eight strings are interleaved, providing protection against bursts.
From the foregoing, it will be noted that a crucial parameter for the ECC to protect the disk is the error-correcting capability t of the RS code. The choice of t is determined by the statistics of errors in the magnetic or optical recording channel. In general, t is chosen in such a way that it provides adequate protection against a worst case of errors in normal operating conditions.
New techniques for magnetic and optical recording involve recording in multiple bands; i.e., an inner band (1), a second band (2) and so on, until reaching the outermost band (m). Usually in multiband recording, the clock frequency of each band is designed to be directly proportional to the inner diameter (ID) of that band. As a result, it is clear that higher error rates will occur on the outer bands than on the inner bands. This is basically due to the fact that the signal detection window is narrower on the outer bands, and the flyheight is higher at the outer bands. Therefore, it can be assumed that the statistical errors rates vary and depend on the band being considered, and that more error protection is required to the data in the outer bands than in the inner bands.
The traditional ECC solution would be to implement a RS code whose error correcting capability t can handle errors in the outer band. However, such a procedure is wasteful. Since the inner bands suffer less errors, they do not require so much redundancy. Another solution would be to implement different codes according to the band being accessed, such as described in U.S. Pat. No. 4,804,959 for the (1,7) and (2,7) run-length-limited codes. While this is feasible, it complicates the hardware significantly.
The most pertinent prior art of which applicants are aware is the paper entitled "Error Control Techniques Applicable to HF Channels", published in the IEEE Proceedings, Vol. 136, Pt. 1, No. 1, Feb. 1989 at pp. 57-63. This paper describes a technique that involves puncturing (deleting) RS codes for a high frequency (HF) channel. In that technique a product code is used adaptively as follows: each row and column are decoded independently. However, instead of transmitting the full row (or column), only a word is transmitted in which f symbols have been punctured. The punctured symbols are treated as erasures and assumed to be zero by the receiver, which calculates the modified syndromes. If these modified syndromes are zero, the receiver concludes that no errors have occurred. If some syndromes are not zero, then the sender sends the additional (previously deleted) redundant bytes and correction is attempted. This technique assumes that communication from receiver to sender is possible, and uses punctured words for detection and not for correction.
Articles published in the May 26, 1988 issue of Electronic Design at pp. 57-60 and published in the Nov. 13, 1986 issue of Electronic Design at pp. 141-144 describe the advantages of constant-density recording for optical and magnetic recording, respectively.
There is a need for an error correction procedure that permits an overall increase in storage capacity by using punctured or deleted bytes and taking advantage of the fact that in magnetic or optical disks the inner bands require different error correction capability than the outer bands. There is also a need for an error correction procedure adapted for use with disk files, where writing and reading of data involve only one-way communication to or from the file, respectively.